The Impact of R5 on Req Calculation

• mabdeljaber
In summary, the addition of the R5 resistor causes R2 and R3 to no longer be shorted, resulting in a different calculation for Req and the initial current through R1. To redraw the circuit with the capacitor as a "short", the capacitor is replaced with a wire. This is because at time t=0, the capacitor is assumed to be uncharged, resulting in a voltage of zero and behaving as a short in the circuit. However, if the capacitor had some initial charge or if the current at another time instant was asked for, the capacitor would not be replaced with a short and differential equations would need to be solved.
mabdeljaber
Homework Statement
Consider the circuit to the right, with R5 = 119 Ω in series with the capacitor. Once again, the switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?
Relevant Equations
I=V/R , Req=R235+R14
So what I know is that without the edition of the R5 resistor R2 and R3 are 0 because the capacitor is short circuiting them. Why does the addition of the R5 resistor cause R2 and R3 to be calculated into the Req for the current equation?

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Delta2
Adding R5 makes a difference because R2 and R3 are no longer shorted. Redraw the circuit with the capacitor as a "short" to find the initial Req and hence the initial current through R1 the usual way.

mabdeljaber
kuruman said:
Adding R5 makes a difference because R2 and R3 are no longer shorted. Redraw the circuit with the capacitor as a "short" to find the initial Req and hence the initial current through R1 the usual way.

Thank you I kind of understand that, but how do I redraw the circuit with the capacitor as a "short". I don't really understand what that looks like

Delta2
mabdeljaber said:
Thank you I kind of understand that, but how do I redraw the circuit with the capacitor as a "short". I don't really understand what that looks like
Replace the capacitor with a wire.

mabdeljaber
gneill said:
Replace the capacitor with a wire.

Thank you! Understood

berkeman
Maybe we have to explain why the capacitor at time t=0 behaves as a short. The reason is that the capacitor is assumed to be uncharged so its voltage is zero at this time instant. So if you apply KVL for the time instant t=0 you ll see that the resulting equation is like that the capacitor is a short.

If the capacitor had some initial charge or if we were asked for the current at another time instant then you shouldn't replace the capacitor with a short. You will had to solve differential equations then (unless the charge of the capacitor at that time instant was given).

1. What is R5 and how does it affect Req calculation?

R5 refers to the fifth resistance in a series circuit. It is used in calculating the equivalent resistance (Req) in a circuit. R5 affects Req calculation by adding to the total resistance, thus increasing the overall resistance in the circuit.

2. Why is R5 important in Req calculation?

R5 is important in Req calculation because it represents one of the resistances in the circuit. In order to accurately calculate the total resistance, all resistances must be taken into account, including R5.

3. How do you calculate Req with R5?

To calculate Req with R5, you must first determine the values of all the resistances in the circuit. Then, use the formula 1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5, where R1-R4 are the other resistances in the circuit. Once you have the value for Req, you can use Ohm's law (V = IR) to calculate the current flowing through the circuit.

4. What happens to Req if R5 is removed from the circuit?

If R5 is removed from the circuit, the total resistance (Req) will decrease. This is because there is now one less resistance in the circuit, resulting in a lower overall resistance.

5. Can R5 have a negative impact on Req calculation?

Yes, R5 can have a negative impact on Req calculation if it is connected in the wrong direction. In a series circuit, resistances must be connected in the same direction for the total resistance to increase. If R5 is connected in the opposite direction, it will decrease the total resistance and result in an inaccurate calculation of Req.

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